The first-order kinetic transition in the A-${\mathit{B}}_2$ (or Ziff-Gulari-Barshad) surface-reaction model [Phys. Rev. Lett. 56, 2553 (1986)] is investigated using a simulation algorithm (or ensemble) in which the coverage of A is held fixed, while the rate y of A adsorption is allowed to vary. This ensemble allows the metastability loop and spinodal point of the phase transition to be carefully examined. The metastable behavior is found to be in qualitative agreement with the predictions of mean-field theory made by Dickman [Phys. Rev. A 34, 4246 (1986)]. Furthermore, the transition point is precisely determined to be ${\mathit{y}}_2$=0.525 60±0.000 01. The metastable behavior near the spinodal point is also investigated using the standard constant-rate algorithm.

We formulate a theory of the Brownian motion for particle ensembles, whose diffusive evolution is entirely generated by the surrounding random environment. By demanding the validity of the momentum conservation law on all conceivable scales adopted for the investigation of individual particle scattering (collisions) on the medium constituents, we are forced to incorporate the environmental recoil effects in the formalism. The Brownian recoil principle elevates the individually negligible phenomena to the momentum conservation law on the ensemble average. The resultant dynamics of the statistical ensemble is governed by the Schrödinger equation, once the diffusion constant D is identified with ħ/2m.

A model for irreversible adsorption recently studied by Jullien and Meakin [J. Phys. A 25, L189 (1992)] resembles the deposition of slow-moving spherical particles on a flat plane, except that multilayer buildup is not allowed. The adsorption process is more rapid than in the case of random sequential adsorption and reaches a somewhat higher fractional coverage in the jamming limit. We have obtained a density expansion up to third order for the pair density function ${\mathrm{\rho }}^{\mathrm{}\left(2\right)\mathrm{}}$(r,ρ), which agrees well with simulation results up to Θ=0.4 and predicts the long-range structure of the jammed monolayer accurately. We have also calculated the leading terms in the three-particle density function. This result was used to compute the available area fraction φ, which falls off initially as ${\mathrm{\Theta }}^3$, the proportionality constant being 16/9+4 √3 /π+500/9${\mathrm{\pi }}^2$.

We discuss simulations using a recently derived Monte Carlo method which generates the isoenthalpic-isotension-isobaric ensemble or HtN ensemble of classical statistical physics. This method is the Monte Carlo counterpart of the Andersen-Parrinello-Rahman HtN form of molecular dynamics. As an example of the use of HtN Monte Carlo calculations we discuss the calculation of the adiabatic elastic constants and other related thermodynamic properties of a crystalline solid from fluctuation formulas specific to the HtN ensemble and compare with the HtN molecular-dynamics calculation of these same quantities. The agreement of the results with earlier calculations of these quantities using other ensembles supports the inference that our probability density generates the HtN ensemble. For the elastic constants, the HtN Monte Carlo calculations have better convergence properties than the HtN molecular-dynamics calculations but are slower, by at least an order of magnitude, than the ThN and EhN molecular-dynamics and Monte Carlo methods.

The spectral autocorrelation function is evaluated analytically for the Gaussian ensembles of Hamiltonian matrices. A direct comparison of the prediction of these ensembles with experimentally measured spectra is thereby possible. Also computed is the time autocorrelation function of an initially prepared nonstationary state. The repulsion of eigenstates in the time domain is clearly manifested in the analytic result.

Several versions of a simplified oblique incidence ballistic deposition model introduced by Nagatani [J. Phys. A 24, L449 (1991)] have been explored using computer simulations and theoretical approaches. In these models self-similar columnar patterns characterized by an algebraic distribution of heights evolve as a consequence of the competition among columns for the incoming flux. The growth rate of each column is a nonlinear function of its height. The competition is driven by the shot noise in the deposition process or, for a deterministic version of the model, by the amplification of disorder in the initial state of the surface. We find excellent agreement between simulation results and the theoretical analysis. However, our results appear to differ substantially from those obtained by Nagatani using smaller-scale simulations and a Monte Carlo renormalization-group analysis. In particular, we indicate how a spurious dependence of the height distribution exponent on the angle of incidence may arise from crossover effects. In the deterministic case the height distribution exponent depends continuously on the distribution of initial disorder.

Particle-decay processes in a nonhyperbolic Hamiltonian system are typically characterized by algebraic laws. That is, for a fixed set of parameter values, if one initializes a particle in a chaotic region near some Kol’mogorov-Arnol’d-Moser (KAM) tori, the probability for this particle to remain in the region at time t decays with time algebraically: P(t)∼${\mathit{t}}^{\mathrm{-}\mathit{z}}$, where z is the decay exponent. As a system parameter varies, the numerically calculated exponent z exhibits rather large fluctuations. In this paper we examine the dynamical origin of such fluctuations using a model system which exhibits unbounded chaotic dynamics (i.e., chaotic scattering). Our results indicate that the fluctuating behavior of z, as a function of the parameter, can be attributed to the breakup of KAM surfaces in phase space. A particularly interesting finding is that, when the outermost KAM surfaces enclosing some central island transform from absolute barriers to partial barriers (Cantori), as the parameter varies, the survival probability P(t) displays two different regions of scaling behavior with different decay exponents. The time scale where this crossover takes place is found to coincide with the typical time for a particle to penetrate the newly created Cantori.

We develop an algorithm to simulate a Gaussian stochastic process that is non-δ-correlated in both space and time coordinates. The colored noise obeys a linear reaction-diffusion Langevin equation with Gaussian white noise. This equation is exactly simulated in a discrete Fourier space.

We investigate the behavior of a chain of N nonlinear oscillators, in a model originally invoked to describe depinning of switching charge-density waves. The dynamics is dominated by the coexistence of a large number of attractors, one of which–the minimally stable state–plays a central role. At threshold, very broad depinning-time distributions occur for long chains. Physically, these long times reflect very slow motion punctuated by rapid but localized motion of the chain.

We extend the stick-slip model of a one-dimensional fault to include the deformation effects of the two-dimensional earth’s crust, which is assumed to be driven by a viscous fluid flow under the crust. Numerical simulations demonstrate that the model shows the Gutenberg-Richter law and the Omori law simultaneously.

A quantum calculation of the third virial coefficient of a two-dimensional gas obeying fractional statistics is performed by diagonalizing the three-body Hamiltonian in a harmonic-oscillator potential with a large fermionic basis. The numerical results for the virial coefficient ${\mathit{A}}_3$ as a function of the flux strength α (α=0 for fermions, α=1 for bosons) are reliable in the range 0≤α≤0.25. $A sub 3— increases quadratically with α for very small α, but higher powers contribute substantially for large α.

The modified Eddington approximation, introduced in 1969 by Pomraning [J. Quant. Spectrosc. Radiat. Transfer 9, 407 (1969)], is used for solving the radiative-transfer equation for plane-parallel media. The specific intensity I(x,μ) is expressed as the sum of an even and an odd function of the angular variable μ, i.e., I(x,μ)=E(x)ε(x,μ)+F(x)o(x,μ); the integro-differential transport equation is thereby transformed into two coupled first-order differential equations involving the energy density E(x), the radiative flux F(x), and D(x)≡${\mathcal{F}}_{\mathrm{-}1}^1$${\mathrm{\mu }}^2$ε(x,μ)dμ. In Pomraning’s treatment, one of these two exact equations is replaced by an approximate version derived by neglecting the spatial dependence of D(x); despite this simplification, the coupled equations usually defy, if one is treating inhomogeneous media, attempts at analytic solutions; the boundary conditions for the two differential equations are fabricated by multiplying the condition satisfied by I(x,μ) at each boundary by a prescribed weight function and integrating with respect to μ. We also outline an alternative strategy wherein the integral equations satisfied by D(x), E(x), and F(x) are deduced and solved by means of the variational method. The advantages of the latter approach are twofold. First, since the pertinent boundary conditions are automatically incorporated in the integral equations, the problem of inferring suitable weight functions is obviated; second, the spatial dependence of D(x) is taken into account explicitly. Numerical results are presented to illustrate the performance of the adapted Pomraning-Eddington approach.

We present a self-consistent scheme to study the localization of a light particle obeying quantum mechanics immersed in classical simple fluids. The interparticle correlations between the particles of the host fluid are analyzed with the Percus-Yevick approximation using the Lennard-Jones potential. The interaction between the light particle and the fluid particles is represented by a contact potential. The Percus-Yevick approximation is also used to describe the density distribution of the fluid particles around the light particle. The effective potential acting on the light particle and the wave function of the light particle are self-consistently determined by the coupled Percus-Yevick and Schrödinger equations. The formalism was used to investigate ortho-positronium localization and annihilation in liquids He and Ne. The theory is found to be in fairly good agreement with existing experiments.

Neutron-diffraction experiments on liquid DI, HI, and on an equimolar mixture of HI and DI are presented. All these three samples were in the same thermodynamic state corresponding to the orthobaric liquid at T=253 K. The three partial structure factors ${\mathit{S}}_{\mathrm{II}}$(Q), ${\mathit{S}}_{\mathrm{HI}}$(Q), ${\mathit{S}}_{\mathrm{HH}}$(Q) are derived exploiting the standard isotopic substitution procedure. The corresponding pair correlation functions ${\mathit{g}}_{\mathrm{II}}$(r), ${\mathit{g}}_{\mathrm{HI}}$(r), and ${\mathit{g}}_{\mathrm{HH}}$(r) are evaluated and compared with those given by a model that neglects all orientational correlations. Our data indicate that ${\mathit{g}}_{\mathrm{II}}$(r) (which is essentially the center-center correlation function) is well reproduced by the pair distribution function of a monatomic Lennard-Jones fluid and that ${\mathit{g}}_{\mathrm{HI}}$(r) (which should be sensitive to the correlations between molecular and intermolecular axes) is very similar to the one derived neglecting orientational correlations. On the contrary, orientational correlations between the molecular axes are clearly present in the ${\mathit{g}}_{\mathrm{HH}}$(r), which deviates significantly from the uncorrelated model results. These facts are consistent with the idea that H bonding is not present in liquid HI and indicate also that the only relevant terms of the anisotropic intermolecular potential are those due to the electric multipolar interactions.

The stationary electron Boltzmann equation is solved for high reduced electric-field strengths E/${\mathit{n}}_0$. We consider both the cases of a homogeneous system and of a Townsend ionization avalanche (exponentially growing electron density). The usual calculation scheme based on the two-term spherical-harmonic expansion fails due to the formation of runaway electrons at high energies. To account for this effect, the velocity space is separated into different energy regions. For energies below the ‘‘runaway threshold’’ (v<${\mathit{v}}_{\mathit{R}}$) Boltzmann’s equation is solved by a modification of the usual calculation scheme. The expansion breaks down near the runaway threshold. For v>${\mathit{v}}_{\mathit{R}}$ we construct an alternative expansion that is suitable to describe the formation of a runaway beam. In the homogeneous case, the runaway flux excludes exactly stationary solutions. Under avalanche conditions, the runaway effect is ‘‘hidden’’ because the runaways follow a Maxwellian distribution. Nevertheless, it has a distinct influence on the ionization coefficient α. This is demonstrated with numerical results for a weakly ionized He plasma, where α decreases strongly with E for high E/${\mathit{n}}_0$ values.

Convective patterns in laterally extended rotating cells with a vertically broken symmetry are analyzed. A simplified model allows one to determine the stability of different basic patterns. By means of a generalized Swift-Hohenberg equation one can study the pattern evolution for different rotation rates and different values of the symmetry-breaking term. In particular, a hexagonal pattern with oscillating amplitudes is analyzed and the role of the defects is discussed.

The multifractal model of turbulence assumes a concentration of the field of vorticity magnitude on a set of dimension smaller than 3. We examine the mechanism for the exponential growth of the vorticity magnitude, and estimate the fractal dimenison of its level sets on the basis of the equations of fluid mechanics. We propose a model of multifractal turbulence in which there is a connection between the fractal dimension of the level sets and the information dimension ${\mathit{D}}_1$ of the carrier of the field of vorticity magnitude. Under the stated conditions we can estimate the dimension ${\mathit{D}}_1$ and evaluate, within the framework of the multifractal model of turbulence, the values of the scaling exponents of velocity and temperature structure functions. We find exponents that are consistent with the available experimental information and which differ from the ones obtained by the Kolmogorov dimensional analysis.

Steady-state and time-dependent two-dimensional thermal convection in a Boussinesq, infinite-Prandtl-number fluid with stress-free boundaries has been investigated. Two independent numerical methods have been employed to calculate the evolution of convective flows in a rectangular box with aspect ratio λ=1.8 in a Rayleigh-number (Ra) range of ${10}^6$${10}^9$. With increasing Ra, greater than ${10}^7$, the flow reveals the presence of disconnected thermals, rather than connected plumes, driven by a persistent large-scale circulation. Such features have also been reported from laboratory convection experiments in the regime of hard turbulence. Extensive calculations were performed (up to 140 overturns) in order to reach the statistically stationary regime for strongly chaotic flows. A Gaussian distribution with a mean value ${\mathrm{Nu}}_{\mathit{t}}$ was derived from the time history of the Nusselt (Nu) numbers. The value of ${\mathrm{Nu}}_{\mathit{t}}$ can be directly obtained by solving the steady-state equations via an iteration procedure. Thus the stationary flow obtained from the steady-state method resembles the turbulent flow in a statistical sense. Since the iteration procedure is about ${10}^4$ times faster than calculating the full time-dependent evolution, it allows for the systematic investigation of the heat-transfer Nu-Ra relationship and other types of scaling laws. The steady-state and time-dependent experiments indicate that a power-law exponent of β=0.315 holds for the Nu-Ra relation for stress-free boundaries in the entire range of Ra. No indication of a jump in the exponent was found in the transition to hard turbulence.

Three-dimensional convection in a rotating fluid layer is studied near the onset of a steady-state instability using equivariant bifurcation theory. The pattern selection problem is formulated as a bifurcation problem on a hexagonal lattice. Symmetry considerations determine the form of the ordinary-differential equations governing the evolution of the marginally stable modes. From the symmetry analysis the relative stability of the primary patterns can be determined. The theory is illustrated explicitly for idealized boundary conditions and the bifurcation diagrams given for all values of the Taylor and Prandtl numbers.

The problem of interaction locality in k space is studied in a diagrammatic perturbation approach for the Navier-Stokes equation in quasi-Lagrangian variables. Analyzing the whole diagram series we have found an exact relation between the asymptotic behavior of the triple-correlation function of velocities that governs the energy transfer over scales and the double-correlation function giving the energy distribution. Namely, at r≪R, we obtain ${\mathit{S}}_3$(r,R,R-r)∝${\mathit{S}}_2$(R)(r/R) [${\mathit{S}}_3$(r)/${\mathit{S}}_2$(r)]∝${\mathit{R}}_2^{\mathrm{\zeta }}$-1${\mathit{r}}_2^{2\mathrm{-}\mathrm{\zeta }}$, where ${\mathrm{\zeta }}_2$ is the static exponent of double-velocity moment. This relation between two different physical quantities (in principle, measurable independently) is accessible to an experimental check. Also, this relation allows us to describe an energy exchange between distant scales in k space: For any steady spectrum carrying constant energy flux, the interactions of the given k-eddies with large (${\mathit{k}}_1$≪k) and small eddies (${\mathit{k}}_2$≫k) are shown to decrease by the same law with the distance in k space, such as (${\mathit{k}}_1$/k${)}_2^{2\mathrm{-}\mathrm{\zeta }}$ and (k/${\mathit{k}}_2$${)}_2^{2\mathrm{-}\mathrm{\zeta }}$. It means a balance of interactions for such a spectrum. Considering, in particular, the multifractal picture of developed turbulence, we analyze the range of exponents h of the velocity field [δv(r)∝${\mathit{r}}^{\mathit{h}}$] which provides the locality of interaction in the k space. It is shown that the condition of infrared locality of interaction (with larger ${\mathit{k}}_1$-eddies) could give only the upper restriction for the exponent. The upper limit thus found (${\mathit{h}}_{\max }$=1) coincides with the boundary exponent of singularity of energy dissipation. As far as an interaction locality in the ultraviolet limit (${\mathit{k}}_2$≫k) is concerned, we prove that any reasonable dimension function D(h) provides locality whatever small h is considered.